AP Style Problem - 13 A ladder 20 feet long is leaning AP Style Problem - 15 A space shuttle is rising vertically at a rate of 2 miles per second. A man against the wall of a house (see figure). The base of the who is 5 miles from the launch point is observing the space shuttle. If @ is the angle of ladder is pulled away from the wall at a rate of 2 feet per elevation, find the rate of change in the angle of elevation at 5 seconds after launch. second. (a) How fast is the top of the ladder moving down the wall when its base is 12 feet from the wall? (b) Consider the triangle formed by the side of the house, the ladder, and the ground. Find the rate at which the area of the triangle is changing when the base of the ladder is 12 feet from the wall. AP Style Problem - 16 The radius and height of a right circular cylinder are found at a certain instant to be 10cm and 20cm respectively. If the radius of the cylinder is increasing at the rate of 2cm/sec, what change in height will keep the volume constant? (c) Find the rate at which the angle between the ladder and the ground is changing when the base of the ladder is 12 feet from the wall. AP Style Problem - 14 Water drains from a conical tank at the of 10 cm. rate of 5 ft /min. The conical tank has radius of 4cm and height (a) What is the relation between the variables h and r? (b) How fast is the water level dropping when h = 5 ft? (c) At what rate is the exposed surface area of the water changing when h = 5 ft?AP Style Problem - 3 A right circular cylinder can is to be designed to hold 27 cubic inches of water. If a minimum amount of material is to be used to construct the can, what must be the radius, in inches, of the can? Justify your answer. V = Torah = 27 h = 21 TCY 2 SA = 27tr + 2 Ter ( 21 AP Style Problem - 8 A man is in a boat 3 miles from the nearest point on the coast and that point is 5 miles away from a resting place on the coast. He plans to row the boat straight to a certain point on the coast and then walk along the coast to reach the resting place. If he can row at 2 miles per hour and walk at 4 miles per hour, toward what point on the coast should he row in order to reach his resting place in the shortest amount of time? distance time = Speed 3 mi moh time = 19+7 ( 2 + 5-X 4mph 2 4 5-X - 5 ml f ( x ) = EXAMPLE 2. If a + = = 25 and - S, what is the value of "when x = 3 and y = 4? 2x+ 2vdy- ax = 0 6+ 8 dy ax 120 dy dx = 8 AP Style Problem - 10 A circular disc is heated so that its radius increases at a rate of 2 cm/s. When the disc is 10 cm in radius, find (a) the rate of change of the disk's circumference. dr = Q , 1 = 10 de = 12TC b) the rate of change of the disk's area. A = Trz = 2TEr